The issue is just that set abstract terms _are_ definite descriptions.
Instead of "the x such that ..." you are talking about "the set
containing all and only x such that ...".
And of course, neither argument is clearly valid. It seems that the
identity is logically equivalent to either s or t only on the
Russellian reading of definite descriptions - but in that case, the
definite descriptions aren't referring terms at all, so they can't
co-refer. So one of the two types of substitution is blocked on any
reading. (Unless there is a referential reading of definite
descriptions that can make the whole sentence equivalent to something
simpler.)
Best,
Kenny Easwaran
On 9/28/06, A.S.Virdi at lse.ac.uk <A.S.Virdi at lse.ac.uk> wrote:
>>> Dear FOMers,
>> Can anyone think of any significant mathematical difference between the
> following two arguments?
>> 1. s Premise
> 2. {x: x = d & s} = {x: x = d} From 1., given substitution salva
> veritate of logical equivalents
> 3. {x: x = d & t} = {x: x = d} From 2., given substitution salva
> veritate of co-referring terms
> 4. t From 3., given substitution salva
> veritate of logical equivalents
>> And (with i is the iota/definite-description operator)
>> 1. s Premise
> 2. ix(x = d & s) = ix(x = d) From 1., given substitution salva
> veritate of logical equivalents
> 3. ix(x = d & t) = ix(x = d) From 2., given substitution salva
> veritate of co-referring terms
> 4. t From 3., given substitution salva
> veritate of logical equivalents
>> Both arguments seem valid (don't they?). So why has there been much
> philosophical ado about nothing concerning the status of definite
> descriptions in setting up this slingshot argument? Replace definite
> descriptions with their set abstract counterparts and there are no
> iota-expressions to be concerned with. Am I missing something here?
>> Arhat Virdi
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